Improved bounds for the number of forests and acyclic orientations in the square lattice

In a recent paper Merino and Welsh (1999) studied several counting problems on the square lattice $L_n$. The authors gave the following bounds for the asymptotics of $f(n)$, the number of forests of $L_n$, and $\alpha(n)$, the number of acyclic orientations of $L_n$: $3.209912 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.84161$ and $22/7 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.70925$. In this paper we improve these bounds as follows: $3.64497 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.74101$ and $3.41358 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.55449$. We obtain this by developing a method for computing the Tutte polynomial of the square lattice and other related graphs based on transfer matrices

Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]

In this paper we prove the asymptotic formula for the moments of Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is to demonstrate that certain a variation of a Laplace method is applicable in this problem, hence the task reduces to a number of technical calculations.Comment: 11 pages, 1 figure (final version). Lithuanian Math. J. (to appear

Factors of sums and alternating sums involving binomial coefficients and powers of integers

We study divisibility properties of certain sums and alternating sums involving binomial coefficients and powers of integers. For example, we prove that for all positive integers $n_1,..., n_m$, $n_{m+1}=n_1$, and any nonnegative integer $r$, there holds {align*} \sum_{k=0}^{n_1}\epsilon^k (2k+1)^{2r+1}\prod_{i=1}^{m} {n_i+n_{i+1}+1\choose n_i-k} \equiv 0 \mod (n_1+n_m+1){n_1+n_m\choose n_1}, {align*} and conjecture that for any nonnegative integer $r$ and positive integer $s$ such that $r+s$ is odd, $$\sum_{k=0}^{n}\epsilon ^k (2k+1)^{r}({2n\choose n-k}-{2n\choose n-k-1})^{s} \equiv 0 \mod{{2n\choose n}},$$ where $\epsilon=\pm 1$.Comment: 14 pages, to appear in Int. J. Number Theor

Proof of two conjectures of Z.-W. Sun on congruences for Franel numbers

For all nonnegative integers n, the Franel numbers are defined as $$f_n=\sum_{k=0}^n {n\choose k}^3.$$ We confirm two conjectures of Z.-W. Sun on congruences for Franel numbers: \sum_{k=0}^{n-1}(3k+2)(-1)^k f_k &\equiv 0 \pmod{2n^2}, \sum_{k=0}^{p-1}(3k+2)(-1)^k f_k &\equiv 2p^2 (2^p-1)^2 \pmod{p^5}, where n is a positive integer and p>3 is a prime.Comment: 8 pages, minor changes, to appear in Integral Transforms Spec. Func

Linear Momentum Density in Quasistatic Electromagnetic Systems

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action-reaction principle, because a non-null external force is required to maintain constant the mechanical linear momentum. We show how one can avoid the divergence in the interaction linear electromagnetic momentum of a system composed by an idealization often used in textbooks (an infinite straight current) and a point charge.Comment: 22 pages, 5 figures, to appear in Eur. J. Phy

MiR-155 has a protective role in the development of non-alcoholic hepatosteatosis in mice

Hepatic steatosis is a global epidemic that is thought to contribute to the pathogenesis of type 2 diabetes. MicroRNAs (miRs) are regulators that can functionally integrate a range of metabolic and inflammatory pathways in liver. We aimed to investigate the functional role of miR-155 in hepatic steatosis. Male C57BL/6 wild-type (WT) and miR-155−/− mice were fed either normal chow or high fat diet (HFD) for 6 months then lipid levels, metabolic and inflammatory parameters were assessed in livers and serum of the mice. Mice lacking endogenous miR-155 that were fed HFD for 6 months developed increased hepatic steatosis compared to WT controls. This was associated with increased liver weight and serum VLDL/LDL cholesterol and alanine transaminase (ALT) levels, as well as increased hepatic expression of genes involved in glucose regulation (Pck1, Cebpa), fatty acid uptake (Cd36) and lipid metabolism (Fasn, Fabp4, Lpl, Abcd2, Pla2g7). Using miRNA target prediction algorithms and the microarray transcriptomic profile of miR-155−/− livers, we identified and validated that Nr1h3 (LXRα) as a direct miR-155 target gene that is potentially responsible for the liver phenotype of miR-155−/− mice. Together these data indicate that miR-155 plays a pivotal role regulating lipid metabolism in liver and that its deregulation may lead to hepatic steatosis in patients with diabetes

Revising Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition, criteria for the bipolar disorders: Phase I of the AREDOC project

Objective: To derive new criteria sets for defining manic and hypomanic episodes (and thus for defining the bipolar I and II disorders), an international Task Force was assembled and termed AREDOC reflecting its role of Assessment, Revision and Evaluation of DSM and other Operational Criteria. This paper reports on the first phase of its deliberations and interim criteria recommendations. Method: The first stage of the process consisted of reviewing Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition, and recent International Classification of Diseases criteria, identifying their limitations and generating modified criteria sets for further in-depth consideration. Task Force members responded to recommendations for modifying criteria and from these the most problematic issues were identified. Results: Principal issues focussed on by Task Force members were how best to differentiate mania and hypomania, how to judge ‘impairment’ (both in and of itself and allowing that functioning may sometimes improve during hypomanic episodes) and concern that rejecting some criteria (e.g. an imposed duration period) might risk false-positive diagnoses of the bipolar disorders. Conclusion: This first-stage report summarises the clinical opinions of international experts in the diagnosis and management of the bipolar disorders, allowing readers to contemplate diagnostic parameters that may influence their clinical decisions. The findings meaningfully inform subsequent Task Force stages (involving a further commentary stage followed by an empirical study) that are expected to generate improved symptom criteria for diagnosing the bipolar I and II disorders with greater precision and to clarify whether they differ dimensionally or categorically

Collaborating around digital tabletops: children’s physical strategies from the UK, India and Finland

We present a study of children collaborating around interactive tabletops in three different countries: the United Kingdom, India and Finland. Our data highlights the key distinctive physical strategies used by children when performing collaborative tasks during this study. Children in the UK tend to prefer static positioning with minimal physical contact and simultaneous object movement. Children in India employed dynamic positioning with frequent physical contact and simultaneous object movement. Children in Finland used a mixture of dynamic and static positioning with minimal physical contact and object movement. Our findings indicate the importance of understanding collaboration strategies and behaviours when designing and deploying interactive tabletops in heterogeneous educational environments. We conclude with a discussion on how designers of tabletops for schools can provide opportunities for children in different countries to define and shape their own collaboration strategies for small group learning that take into account their different classroom practices

Peroxisome Proliferator-Activated Receptor-Gamma Agonists Suppress Tissue Factor Overexpression in Rat Balloon Injury Model with Paclitaxel Infusion

The role and underlying mechanisms of rosiglitazone, a peroxisome proliferator-activated receptor-gamma (PPAR-γ) agonist, on myocardial infarction are poorly understood. We investigated the effects of this PPAR-γ agonist on the expression of tissue factor (TF), a primary molecule for thrombosis, and elucidated its underlying mechanisms. The PPAR-γ agonist inhibited TF expression in response to TNF-α in human umbilical vein endothelial cells, human monocytic leukemia cell line, and human umbilical arterial smooth muscle cells. The overexpression of TF was mediated by increased phosphorylation of mitogen-activated protein kinase (MAPK), which was blocked by the PPAR-γ agonist. The effective MAPK differed depending on each cell type. Luciferase and ChIP assays showed that transcription factor, activator protein-1 (AP-1), was a pivotal target of the PPAR-γ agonist to lower TF transcription. Intriguingly, two main drugs for drug-eluting stent, paclitaxel or rapamycin, significantly exaggerated thrombin-induced TF expression, which was also effectively blocked by the PPAR-γ agonist in all cell types. This PPAR-γ agonist did not impair TF pathway inhibitor (TFPI) in three cell types. In rat balloon injury model (Sprague-Dawley rats, n = 10/group) with continuous paclitaxel infusion, the PPAR-γ agonist attenuated TF expression by 70±5% (n = 4; P<0.0001) in injured vasculature. Taken together, rosiglitazone reduced TF expression in three critical cell types involved in vascular thrombus formation via MAPK and AP-1 inhibitions. Also, this PPAR-γ agonist reversed the paclitaxel-induced aggravation of TF expression, which suggests a possibility that the benefits might outweigh its risks in a group of patients with paclitaxel-eluting stent implanted